Multiplicative functionals on ensembles of non-intersecting paths
The purpose of this article is to develop a theory behind the occurrence of “path-integral” kernels in the study of extended determinantal point processes and non-intersecting line ensembles. Our first result shows how determinants involving such kernels arise naturally in studying ratios of partiti...
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| Natura: | Articolo |
| Lingua: | en_US |
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Institute of Mathematical Statistics
2017
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| Accesso online: | http://hdl.handle.net/1721.1/110173 https://orcid.org/0000-0002-2913-5238 |
| _version_ | 1826200493401047040 |
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| author | Borodin, Alexei Corwin, Ivan Remenik, Daniel |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Borodin, Alexei Corwin, Ivan Remenik, Daniel |
| author_sort | Borodin, Alexei |
| collection | MIT |
| description | The purpose of this article is to develop a theory behind the occurrence of “path-integral” kernels in the study of extended determinantal point processes and non-intersecting line ensembles. Our first result shows how determinants involving such kernels arise naturally in studying ratios of partition functions and expectations of multiplicative functionals for ensembles of non-intersecting paths on weighted graphs. Our second result shows how Fredholm determinants with extended kernels (as arise in the study of extended determinantal point processes such as the Airy[subscript 2] process) are equal to Fredholm determinants with path-integral kernels. We also show how the second result applies to a number of examples including the stationary (GUE) Dyson Brownian motion, the Airy[subscript 2] process, the Pearcey process, the Airy[subscript 1] and Airy[subscript 2→1] processes, and Markov processes on partitions related to the zz-measures. |
| first_indexed | 2024-09-23T11:37:19Z |
| format | Article |
| id | mit-1721.1/110173 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T11:37:19Z |
| publishDate | 2017 |
| publisher | Institute of Mathematical Statistics |
| record_format | dspace |
| spelling | mit-1721.1/1101732022-09-27T20:49:29Z Multiplicative functionals on ensembles of non-intersecting paths Borodin, Alexei Corwin, Ivan Remenik, Daniel Massachusetts Institute of Technology. Department of Mathematics Borodin, Alexei Corwin, Ivan The purpose of this article is to develop a theory behind the occurrence of “path-integral” kernels in the study of extended determinantal point processes and non-intersecting line ensembles. Our first result shows how determinants involving such kernels arise naturally in studying ratios of partition functions and expectations of multiplicative functionals for ensembles of non-intersecting paths on weighted graphs. Our second result shows how Fredholm determinants with extended kernels (as arise in the study of extended determinantal point processes such as the Airy[subscript 2] process) are equal to Fredholm determinants with path-integral kernels. We also show how the second result applies to a number of examples including the stationary (GUE) Dyson Brownian motion, the Airy[subscript 2] process, the Pearcey process, the Airy[subscript 1] and Airy[subscript 2→1] processes, and Markov processes on partitions related to the zz-measures. National Science Foundation (U.S.) (Grant DMS- 1056390) National Science Foundation (U.S.) (Grant DMS-1208998) Clay Mathematics Institute (Clay Research Fellowship) Microsoft Research (Schramm Memorial Fellowship) 2017-06-22T18:56:20Z 2017-06-22T18:56:20Z 2015-02 2013-08 Article http://purl.org/eprint/type/JournalArticle 0246-0203 http://hdl.handle.net/1721.1/110173 Borodin, Alexei, Ivan Corwin, and Daniel Remenik. “Multiplicative Functionals on Ensembles of Non-Intersecting Paths.” Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 51, no. 1 (February 2015): 28–58. © 2015 Association des Publications de l’Institut Henri Poincaré https://orcid.org/0000-0002-2913-5238 en_US http://dx.doi.org/10.1214/13-AIHP579 Annales de l Institut Henri Poincaré Probabilités et Statistiques Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Institute of Mathematical Statistics arXiv |
| spellingShingle | Borodin, Alexei Corwin, Ivan Remenik, Daniel Multiplicative functionals on ensembles of non-intersecting paths |
| title | Multiplicative functionals on ensembles of non-intersecting paths |
| title_full | Multiplicative functionals on ensembles of non-intersecting paths |
| title_fullStr | Multiplicative functionals on ensembles of non-intersecting paths |
| title_full_unstemmed | Multiplicative functionals on ensembles of non-intersecting paths |
| title_short | Multiplicative functionals on ensembles of non-intersecting paths |
| title_sort | multiplicative functionals on ensembles of non intersecting paths |
| url | http://hdl.handle.net/1721.1/110173 https://orcid.org/0000-0002-2913-5238 |
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